Final answer to the problem
$-\frac{8}{243}\sqrt{4-9x^2}+\frac{-\left(3x\right)^{2}\sqrt{4-9x^2}}{243}+\frac{1}{2}x^2+C_0$
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Step-by-step Solution
How should I solve this problem?
- Integrate by trigonometric substitution
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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1
Simplifying
$\int\left(\frac{x^3}{\sqrt{4-9x^2}}+x\right)dx$
Learn how to solve problems step by step online.
$\int\left(\frac{x^3}{\sqrt{4-9x^2}}+x\right)dx$
Learn how to solve problems step by step online. Integrate int((x^3)/((4+1*-9x^2)^(1/2))+x)dx. Simplifying. Expand the integral \int\left(\frac{x^3}{\sqrt{4-9x^2}}+x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. First, factor the terms inside the radical by 9 for an easier handling. Taking the constant out of the radical.
Final answer to the problem
$-\frac{8}{243}\sqrt{4-9x^2}+\frac{-\left(3x\right)^{2}\sqrt{4-9x^2}}{243}+\frac{1}{2}x^2+C_0$
